The Cubs want to interview Red Sox bench coach Torey Lovullo for their managerial vacancy and make a decision on the job soon, according to major league sources.

Red Sox general manager Ben Cherington, however, said at a news conference Monday that the Cubs have not asked for permission to interview Lovullo.

What gives?

Evidently this: The Cubs and Red Sox reached an agreement that they would not hire each other’s employees after Theo Epstein left Boston for Chicago in October 2011. That agreement remains in effect, though its exact length is not known. One published report at the time said it was three years.

How the agreement applies to Lovullo is unclear: He was the Red Sox’s Triple A manager under Epstein in 2010, but then spent two seasons on John Farrell’s staff with the Blue Jays. Epstein departed in the interim, and Lovullo did not become a Red Sox employee again until he returned with Farrell in October 2012.

Adding to the complexity: Teams generally allow employees to interview for promotions. For Lovullo, the Cubs’ job certainly would qualify.

The Red Sox, however, apparently are going by the letter of the agreement and balking at the idea of Lovullo interviewing with the Cubs. A resolution, one source said, “will come down to ownership” – meaning a concession by Red Sox ownership or perhaps some kind of special arrangement between the clubs.

The Cubs, who could not even attempt to talk to Lovullo until after the Red Sox won the World Series, might not want to wait much longer. They had intended to make a decision on their next manager by the middle of this week.

The other known candidates for the Cubs’ job are Padres bench coach Rick Renteria, Rays bench coach Dave Martinez, Padres executive and former Arizona Diamondbacks manager A.J. Hinch, former Indians and Nationals manager Manny Acta and former Indians and Mariners manager Eric Wedge.